White plays and wins in 2 moves https://lichess.org/fIB8yxvu
- Kg6 Rd1 2. Rf8#
The analysis board does checkmate in 5 moves
- Kg6 Rg8+ 2. Kh6 Rg6+ 3. Kxg6 Kg8 4. Rf2+ Kh8 5. Rh2#
Using the rook to check extends the game.
Source:
https://www.amazon.com/Chess-Puzzles-Advanced-Expert-Level/dp/B0917YQZP1